we are given
differential equation as

we are given

Firstly, we will find y' , y'' and y'''
those are first , second and third derivative
First derivative is

Second derivative is


Third derivative is


now, we can plug these values into differential equation
and we get

now, we can factor out common terms

we can move that term on right side

now, we can factor out


now, we can set them equal





so, we will get
...............Answer
I don't know if this is the right one but i hope this helps. this is how i learned it.
step 1=get variables on one side oof the equal sign by using inverse operation (add or subtract smaller variable)
step 2= get constants away from variable to the other side of the equal sign by using inverse operations (add or subtract constant)
step 3: isolate the variable using inverse operation (multiply or divide)
All you would have to do is plug in 5 for t since that is the time; then you would see that the height of the object after 5 seconds is 886 ft. Hope this helped!